Business Decision Making - Analysis of Education Qualification and Wage Division
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Added on  2023/06/12
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This report provides a descriptive statistical analysis of the Education qualification division and wage division among people of a region. It includes charts, tables, and hypothesis testing for the average prices of properties in two suburbs of Sydney.
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BUSINESS DECISION MAKING Name of the student: Name of the university: Author’s note:
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Answer 1: ï‚·Population Web institute is interested in checking about the Education qualification division and wage division among people of the said region. It can be said that their is a connection between the two variables and it can be tested here. ï‚·For Wages: Given is the data set for wages. A descriptive statiscal analysis report of the given variable is given below: Table 1: Descriptive analysis of wages. Mean25.61666667 Standard Error0.340206957 Median23.75 Mode25 Standard Deviation7.86165206 Sample Variance61.80557311 Kurtosis4.807383971 Skewness1.57737306 Range60 Minimum10 Maximum70 Sum13679.3 Count534 1st Quartile21.25 3rd Quartile28 IQR6.75 It can be said from the table that the average wage of people in the said are ais 25.616667 and it can vary within a range of 0.3402. Maximum people has the wage of 25 and 25 % people has wage above 28 and 25 % has wages below 21.25 and 50% people have wages in the range of 21.25 and 28. Again, 50% has wages below 23.75 and 50% has wages above 23.75. The maximum wage is 70 and the minimum wage is 10.
A histogram can be posted here depicting distribution of wages. 20-Oct20-3030-4040-5050-6060-70 0 50 100 150 200 250 300 350 400 Wage chart Fig 1: Histogram for wages. It can be said from the histogram that the variable wage has a distribution towards the low wages category. Therefore, the distribution is left tailed. A Pie chart depicting the percentage of people in the different wage group is attached below. 20-Oct 16% 20-30 65% 30-40 15% 40-50 4% 50-60 1%60-70 0% Wage chart Fig 2: Pie chart for wages.
The Pie chart shows percentage of people in the different divisions.The division of 10-20 has 16% of people, the division of 20-30 has 64% of people which is the highest one, the division of 30-40 has 15% of people, the division of 40-50 has 4% of people, the division of 50-60 has 1 %of people and the last division of 60-70 has 0% of people. For Education: A descriptive statistical test depicting data features here can be shown here. Table 2: Descriptive analysis for Education. Mean2.726078799 Standard Error0.042159852 Median2 Mode2 Standard Deviation0.973335773 Sample Variance0.947382528 Kurtosis - 0.364587077 Skewness0.878054936 Range4 Minimum1 Maximum5 Sum1453 Count533 The maximum frequency is of 2 that is people with secondary education and there are 533 people in total. A histogram depicting the distribution of this education division is geiven below:
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PrimarySecondaryBachelorMasterDoctor 0 50 100 150 200 250 300 350 Education chart Fig 3: Chart for education division. The cjhart clearly shows that the dataset is mostly concentrated towards the middle most value that is most of the frequency is in the secondary division and the next two cases like bachelor and ,asater degreeshas wequal divisions ehich is a bit less than the secondary part. The lowest is of the primary part and the second lowest is of doctorate division. Thje data has a concentration in the middle region. A Pie chart depicting the percentage division of people in each of the sections is given below:
Primary 1% Secondary 55%Bachelor 20% Master 18% Doctor 6% Education chart Fig: Pie chart for division in education The Pie chart clearly shows that 1% people in the primary division, 55 % people in the secondary devision, 20 % people in the bachelor division and 18 % people in the masters division, 20% people in the bachelor division and finally 6% peoplein the doctorate division. (3) i. Proportion statistic or the p statistic will be used her. The test statistic will be; [(p – P) /σ] ,
where, p =is the hypothesized value of the statistic, P = calculated value of the statistic, ii. The required null and alternative hypothesis for the test is : H0: p = 0.45 vs. H1: p> 0.45. iii. Primary and secondary education can be considered here as tertiaryeducation.Thereareintotal299peopleinthesaid group. Therefore, proportion of people in the said group is 0.56, which is the required calculated proportion. Therefore, the value of the test statistic will be 5.11. The statistic is to tested at 5% level of significance. Therefore, thetestsignificantvalueis1.96,whichislessthanthetest statisticvalue.Therefore,thenullhypothesiscanberejected hereanditcanbeconcludedthattheproportionoftertiary education has increased. (4) i. Mean test statistic or the t- statistic will be used her. The required test statistic is: t = (M – m)/σ/√n where, m =is the hypothesized value of the statistic, M = calculated value of the statistic, n= Total number of observation
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σ = Population standard deviation. ii. The required null and alternative testing hypothesis is : H0: t = 30 vs. H1: t≠30. iii.The calculated value of the t statistic is 173.714. The statistic will be tested atb 55 level of significance and the normal value at 55 level of significance is 1.96 which is less than the hypothesized value. Therefore, the null hypothesiscan be rejected hereand it can be said that the average per hour wage is not 30. Answer 2: (1)The required dataset is: Table 3: House prices. Houses House Price - Subnurb 1 House Price - Suburb 2 110501350 21600870 312951250 41150800 51000720 611001000 7650535 81200525 91150630 10895700
11840620 12560975 131250725 14675660 152500965 16775550 1714501700 181095780 202000560 21870880 22450700 2313501100 24550850 25750900 268401650 27750570 28450650 291150550 301150670 311150730 32850530 33520470 345503500 3611001700 37850720 39730550 40470720 (2)The test require dataset from the two suburbs of Sydney named NEWTOWN and HURSTVILLE. The datasrt are the prices of the 3bhk apartment in th said place and are to be tested for the average prices of the properties. The hypothesis to be tested here are : H0: k1=0 vs H1:k1>0, where k1=m1-m2.
where, m1 = mean of suburb 1 and m2 = mean of the suburb 2. It can be seen from the table here that the t-statistic value is 0.648 and the 2 tailed t significant value is 1.96. Therefore, the significant value is greater than the statistical value and the null hypothesis can be accepted here and it can be said that the average prices are equal in both the regions. Therefore, the test result is that the average prices are equal in both the regions.